Method and apparatus for maintaining proper noble metal loading for a noble metal application process for water-cooled nuclear reactors

ABSTRACT

A non-steady state computer model of water in a Boiling Water Reactor (BWR) primary water flow circuit is used to represent the water chemistry and noble metal loading during, for example, an in situ noble metal application process. The modeling software is provided on a laptop or portable computer for real-time use in the field at different reactor sites. After inputting data representing the initial state of reactor water chemistry and operating conditions of the reactor, the model determines the water chemistry, pH, conductivity and noble metal loading throughout the BWR primary water flow circuit, including selected sample locations, as a function of time. Results are used to determine whether technical specifications on conductivity or other chemistry-related parameters will be exceeded during the noble metal application process. Values of rate constants used for modeling noble metal reactions may be changed on site at the reactor during the application process.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Applicationserial No. 60/173,562, filed Dec. 30, 1999, the entire content of whichis incorporated by reference into this application.

TECHNICAL FIELD OF THE INVENTION

This invention relates generally to reducing the corrosion potential ofcomponents exposed to high-temperature water through a noble metalapplication process. More specifically, the invention relates to amethod and apparatus for modeling and maintaining the amount of noblemetals deposited in the water circuit of a boiling water reactor andcomponents thereof during an in situ noble metal application process.

BACKGROUND OF THE INVENTION

Nuclear reactors are used in electric power generation, research andpropulsion. A reactor pressure vessel contains the reactor coolant, i.e.water, which removes heat from the nuclear core. Respective pipingcircuits carry the heated water or steam to the steam generators orturbines and carry circulated water or feedwater back to the vessel.Operating pressures and temperatures for the reactor pressure vessel areabout 7 MPa and 288EC for a boiling water reactor (BWR), and about 15MPa and 320EC for a pressurized water reactor (PWR). The materials usedin both BWRs and PWRs must withstand various loading, environmental andradiation conditions.

Some of the materials exposed to high-temperature water include carbonsteel, alloy steel, stainless steel, nickel-based, cobalt-based andzirconium-based alloys. Despite careful selection and treatment of thesematerials for use in water reactors, corrosion occurs in the materialsexposed to the high-temperature water. Such corrosion contributes to avariety of problems, e.g., stress corrosion cracking, crevice corrosion,erosion corrosion, sticking of pressure relief valves and buildup of thegamma radiation-emitting Co-60 isotope.

Stress corrosion cracking (SCC) is a known phenomenon occurring inreactor components, such as structural members, piping, fasteners andwelds exposed to high-temperature water. As used herein, SCC refers tocracking propagated by static or dynamic tensile stressing incombination with corrosion at the crack tip. The reactor components aresubject to a variety of stresses associated with, e.g., differences inthermal expansion, the operating pressure needed for the containment ofthe reactor cooling water, and other sources such as residual stressfrom welding, cold working and other asymmetric metal treatments. Inaddition, water chemistry, welding, heat treatment, and radiation canincrease the susceptibility of metal in a component to SCC.

It is well known that SCC occurs at higher rates when oxygen is presentin the reactor water in concentrations of about 5 ppb or greater. SCC isfurther increased in a high radiation flux where oxidizing species, suchas oxygen, hydrogen peroxide, and short-lived radicals, are producedfrom radiolytic decomposition of the reactor water. Such oxidizingspecies increase the electrochemical corrosion potential (ECP) ofmetals. Electrochemical corrosion is caused by a flow of electrons fromanodic to cathodic areas on metallic surfaces. The ECP is a measure ofthe thermodynamic tendency for corrosion phenomena to occur, and is afundamental parameter in determining rates of, e.g., SCC, corrosionfatigue, corrosion film thickening, and general corrosion.

In a BWR, the radiolysis of the primary water coolant in the reactorcore causes the net decomposition of a small fraction of the water tothe chemical products H₂, H₂O₂, O₂ and oxidizing and reducing radicals.For steady-state operating conditions, equilibrium concentrations of O₂,H₂O₂, and H₂ are established in both the water which is recirculated andthe steam going to the turbine. This concentration of O₂, H₂O₂, and H₂is oxidizing and results in conditions that can promote intergranularstress corrosion cracking (IGSCC) of susceptible materials ofconstruction. One method employed to mitigate IGSCC of susceptiblematerial is the application of hydrogen water chemistry (HWC), wherebythe oxidizing nature of the BWR environment is modified to a morereducing condition. This effect is achieved by adding hydrogen gas tothe reactor feedwater. When the hydrogen reaches the reactor vessel, itreacts with the radiolytically formed oxidizing species to reform water,thereby lowering the concentration of dissolved oxidizing species in thewater in the vicinity of metal surfaces. The rate of these recombinationreactions is dependent on local radiation fields, water flow rates andother variables.

The injected hydrogen reduces the level of oxidizing species in thewater, such as dissolved oxygen, and as a result lowers the ECP ofmetals in the water. However, factors such as variations in water flowrates and the time or intensity of exposure to neutron or gammaradiation result in the production of oxidizing species at differentlevels in different reactors. Thus, varying amounts of hydrogen havebeen required to reduce the level of oxidizing species sufficiently tomaintain the ECP below a critical potential required for protection fromIGSCC in high-temperature water. As used herein, the term “criticalpotential” means a corrosion potential at or below a range of values ofabout −0.230 to −0.300 V based on the standard hydrogen electrode (SHE)scale. IGSCC proceeds at an accelerated rate in systems in which the ECPis above the critical potential, and at a substantially lower or zerorate in systems in which the ECP is below the critical potential. Watercontaining oxidizing species such as oxygen increases the ECP of metalsexposed to the water above the critical potential, whereas water withlittle or no oxidizing species presents results in an ECP below thecritical potential.

Corrosion potentials of stainless steels in contact with reactor watercontaining oxidizing species can be reduced below the critical potentialby injection of hydrogen into the water so that the dissolved hydrogenconcentration is about 50 to 100 ppb or greater. For adequate feedwaterhydrogen addition rates, conditions necessary to inhibit IGSCC can beestablished in certain locations of the reactor. Different locations inthe reactor system require different levels of hydrogen addition. Forexample, much higher hydrogen injection levels are necessary to reducethe ECP within the high radiation flux of the reactor core, or whenoxidizing cationic impurities, e.g., cupric ion, are present.

An effective step toward to achieving the goal of reducing ECP withinthe high radiation flux of the reactor core is to either coat or alloythe stainless steel surface with palladium or any other noble groupmetal. As used herein, the term “noble metal” means metals from thegroup consisting of platinum, palladium, osmium, ruthenium, iridium,rhodium, and mixtures thereof. The presence of palladium or other noblemetal on the stainless steel surface catalyzes the recombination ofoxidizing and reducing species in contact with the surface and reducesthe injected hydrogen demand in achieving the required IGSCC criticalpotential of −0.230 V(SHE). Known techniques for palladium coatinginclude electroplating, electroless plating, plasma deposition andrelated high-vacuum techniques. Palladium alloying can also be carriedout using standard alloy preparation techniques. Unfortunately, both ofthese approaches are ex situ techniques in that they cannot be practicedwhile the reactor is in operation.

U.S. Pat. No. 5,135,709 to Andresen et al. discloses a method forlowering the ECP on components formed from carbon steel, alloy steel,stainless steel, nickel-based alloys or cobalt-based alloys which areexposed to high-temperature water by forming the component to have acatalytic layer of a platinum group metal. As used therein, the term“catalytic layer” means a coating on a substrate, or a solute in analloy formed into the substrate, the coating or solute being sufficientto catalyze the recombination of oxidizing and reducing species at thesurface of the substrate.

In nuclear reactors, ECP is increased by the high levels of oxidizingspecies, e.g., up to 200 ppb or greater of oxygen in the water measuredin the circulation piping, produced from the radiolytic decomposition ofwater in the core of the nuclear reactor. The method disclosed in U.S.Pat. No. 5,135,709 further comprises providing a reducing species in thehigh-temperature water that can combine with the oxidizing species. Inaccordance with this known method, high concentrations of hydrogen,i.e., about 100 ppb or more, must be added to the water to provideadequate protection to materials outside the reactor core region, andstill higher concentrations are needed to afford protection to materialsin the reactor core.

The formation of a catalytic layer of a platinum group metal on an alloyfrom the aforementioned group catalyzes the recombination of reducingspecies, such as hydrogen, with oxidizing species, such as oxygen orhydrogen peroxide, that are present in the water of a BWR. Suchcatalytic action at the surface of the alloy can lower the ECP of thealloy below the critical potential where IGSCC is minimized. As aresult, the efficacy of hydrogen additions to high-temperature water inlowering the ECP of components made from the alloy and exposed to theinjected water is increased many-fold. Furthermore, it is possible toprovide catalytic activity at metal alloy surfaces if the metalsubstrate of such surfaces contains a catalytic layer of a platinumgroup metal. Relatively small amounts of the platinum group metal aresufficient to provide the catalytic layer and catalytic activity at thesurface of the metal substrate.

Thus, lower amounts of reducing species such as hydrogen are effectivein reducing the ECP of the metal components below the criticalpotential, because the efficiency of recombination of oxidizing andreducing species is increased many-fold by the catalytic layer. Reducingspecies that can combine with the oxidizing species in thehigh-temperature water are provided by conventional means known in theart. In particular, reducing species such as hydrogen, ammonia, orhydrazine are injected into the feedwater of the nuclear reactor.However, a need still exists to provide for improved control over thedeposition of platinum, palladium or other catalytic metals onto thesurface of components in situ. The present invention seeks to satisfythat need.

In this regard, it has been discovered that it is possible to controlthe amount of metal species deposited on metal surfaces by carefullycontrolling the water temperature into which the metal is introducedwithin a particular temperature range. It has also been discovered, thatby careful selection of the water temperature, metal concentration andtime, it is possible to control the deposit ratio of a particular metalfrom a mixture of metals.

In addition, it has been found that an unexpectedly increased loading ofthe deposited metal occurs when the temperature of the water is selectedto be within the range of about 200° F. to 550° F., more particularlywithin the range of about 300° F. to about 450° F., as compared to theloading obtained at temperatures above or below that range. This allowsfor the selection of a particular metal loading on the metal surface bya careful selection of the appropriate water temperature into which thecompound containing the metal species to be deposited is introduced. Thedeposited metal is typically a noble metal and is introduced in theabsence of hydrogen or other added reducing agents.

Moreover, the above described process may be carried out in the presenceof hydrogen and other reducing agents. For example, commonly assignedwith the present invention, U.S. Pat. Nos. 5,600,691 and 5,818,893 teachan in situ noble metal application process, forming the basis of what isgenerically referred to herein as the NobleChem™ process, wherebypalladium or other catalytic metals are deposited onto stainless steelor other metal surfaces immersed in high-temperature water such that thecatalytic metal penetrates into existing cracks in the metal surfaces.During this NobleChem™ process, noble or other catalytic metals areadded to the water coolant in the reactor core as a metal-containingcompound that is introduced in an amount such that, upon decompositionof the metal-containing compound in the water, the metal atoms arereleased in an amount sufficient, when present on the metal surface, toreduce the electrochemical corrosion potential of the metal to a levelbelow the critical potential, and thereby protect against intergranularstress corrosion cracking.

Basically, the NobleChem™ process provides a method for reducingcorrosion of alloy components such as stainless steel components, in awater-cooled nuclear reactor or associated components, wherein asolution of a compound containing a noble metal (or other catalyticmetals) is injected into the reactor water at a temperature of about to200° to 550° F., for example about 300° to 450° F., in an amount suchthat, upon decomposition of the compound under the operating reactorthermal conditions, atoms of the metal compound are released at a ratesuch that the concentration of the metal in the water is sufficient,once incorporated on the alloy components, to reduce the electrochemicalcorrosion potential of the alloy components to a level below thecritical potential. Hydrogen may be present at low levels, for example,preferably less than 400 ppb but acceptably about 300-600 ppb. In thisway, the alloy reactor components are protected against intergranularstress corrosion cracking.

The above described NobleChem™ process is based on the discovery that itis possible to control the amount of metals deposited on an oxidizedmetal surface in high temperature water, as well as the ratio of metaldeposit from a mixture of metals, by careful choice of the temperatureof the water, concentration of the metal and time. Generally, thepreferred noble metals used for the NobleChem™ process are incorporatedinto a compound containing platinum and rhodium. For example, with aplatinum/rhodium mixture, the weight ratio within the temperature rangeof 200° F.-550° F. is typically from about 5:1 to about 40:1platinum:rhodium. The compound has the property that it decomposes inthe high-temperature water to release atoms of the metal whichincorporate in the oxide film at a particular loading level.

Compounds of the platinum group metals are preferred. The term “aplatinum group metal”, as used herein, means platinum, palladium,osmium, ruthenium, iridium, rhodium and mixtures thereof. It is alsopossible to use compounds of non-platinum group metals, such as forexample zinc, titanium, zirconium, niobium, tantalum, tungsten andvanadium. Mixtures of platinum group compounds may also be used.Mixtures of platinum group compounds and non-platinum group compoundsmay also be used in combination, for example platinum and zinc. Thecompounds may be organo-metallic, organic or inorganic and may besoluble or insoluble in water (i.e. may form solutions or suspensions inwater and/or other media such alcohols and/or acids). Generally, whenmixtures of platinum and non-platinum group metals are used, theplatinum group metal is in excess of the other metal.

Examples of preferred platinum group metal compounds which may be usedand examples of mixtures of the compounds which may be used arediscussed in greater detail in the above mentioned patents. Use of suchmixtures results in the incorporation of various noble metals in theoxidized stainless steel surfaces within the reactor.

The noble metal-containing compound is injected in situ into thehigh-temperature water of a BWR (or PWR) in an amount such as toproduce, upon decomposition of the compound, a metal concentration of upto 2000 ppb, for example about 1 to 850 ppb, more usually 5 to 100 ppb.The high temperatures as well as the gamma and neutron radiation in thereactor core act to decompose the compound, thereby freeing noble metalions/atoms for deposition on the surface of the oxide film. (As usedherein, the term “atoms” means atoms or ions).

The noble metal injection solution may be prepared for example bydissolving the noble metal compound in ethanol. The ethanol solution isthen diluted with water. Alternatively, a water-based suspension can beformed, without using ethanol, by mixing the noble metal compound inwater.

The noble metal either deposits or is incorporated into the stainlesssteel oxide film via a thermal decomposition process of the noble metalcompound. As a result of that decomposition, noble metal ions/atomsbecome available to replace atoms, e.g., iron atoms, in the oxide film,thereby producing a noble metal-doped oxide film on stainless steel.

The noble metal-containing compound may be injected directly into thewater of the reactor in situ in the form of an aqueous solution orsuspension, or may be dissolved in the water before it is introduced tothe reactor. For the sake of this discussion, the term “solution” meanssolution or suspension. Such solutions and suspensions may be formedusing media well known to those skilled in the art. Examples of suitablemedia in which solutions and/or suspensions are formed, are water,alkanols such as ethanol, propanol, n-butanol, and acids such as lowercarboxylic acids, e.g. acetic acid, propionic acid and butyric acid.

U.S. Pat. No. 5,818,893, entitled “In-Situ Palladium Doping Or CoatingOf Stainless Steel Surfaces”, which is commonly assigned with thepresent invention and incorporated herein by reference, discusses theeffect of variation of temperature on metal deposit loading rate ingreater detail, as well as the effect of distance from the point ofintroduction of the compound to the region of deposit on the metalsurface. As demonstrated in that patent, an enhanced loading is observedover the temperature range of 200° to 500° F., more especially in therange of 300° to 450° F., and particularly at about 340° to 360° F. Theloading observed in the temperature range of 300 to 450° F. extends fromabout 10 μg/cm² at about 300° F. to a maximum of about 62 μg/cm² atabout 340° F., and then drops off to about 10 μg/cm² and lower as thetemperature rises towards 500° F. This peaking effect is surprising andaffords the advantage that loading of the metal species on the metalsurface can be controlled by careful selection of the water temperatureand point of introduction of the metal to be deposited.

When the metal compound solution or suspension enters thehigh-temperature water, the compound decomposes very rapidly to produceatoms, which are incorporated into the metal (typically stainless steel)oxide film. In accordance with the above described process, only thesolution or suspension of the compound is introduced into thehigh-temperature water initially. No further agents, such as hydrogen,other reducing agents, acids or bases are introduced into thehigh-temperature water when the compound solution or suspension isinjected into and decomposes in the high-temperature water.

The presence of rhodium renders the deposit more durable. However, itwas found that as the temperature of water in the reactor reaches 300°to 500° F., the ratio of deposited platinum to rhodium drops to withinthe range of about 5:1 to 10:1. Thus, knowing this relationship, it ispossible to control the ratio of platinum to rhodium in the depositedlayer based on the prevailing temperature conditions of the water. Inaddition, the deposition rate for a 60 ppb platinum and 20 ppb rhodiumsolution is a negative exponential with temperature in the 180 to 350°F. range. Thus, it is possible to predict the effect of temperature onthe ratio of deposit of the metals and the time required to deposit agiven quantity of noble metal in the oxide. Accordingly, the bulkconcentration of platinum and rhodium, time and temperature are allcontrollable variables that may be used to produce a desiredplatinum-to-rhodium deposit ratio and a desired total noble metalloading.

The noble metal-containing compound solution or suspension may beinjected into the high-temperature water while the reactor is operatingand generating nuclear heat (full power operation), or during cool down,during outage, during heat-up, during hot standby, or during low poweroperation. Preferably, the noble metal is introduced into residual heatremoval (RHR) piping, recirculation piping, feedwater line, core delta Pline, jet pump instrumentation line, control rod drive cooling waterlines, water level control points, or any other location which providesintroduction of the noble metal into the reactor water and good mixingwith the water. As used herein, the term “high-temperature water” in thepresent invention means water having a temperature of about 200° F. orgreater, steam, or the condensate thereof. High temperature water can befound in a variety of known apparatus, such as water deaerators, nuclearreactors, and steam-driven power plants. The temperature of the waterwhen noble metal is added to the reactor water is typically in the rangeof 200-500° F., for example 200-450° F., more usually about 340°-360° F.When the noble metal-containing compound is in the high-temperaturewater, it decomposes very rapidly and the metal atoms are incorporatedin the oxide surface.

Preferably, only very dilute compound solution or suspension is injectedinto the high-temperature water. No reducing agents (includinghydrogen), acids and bases, are added. As a result, the typical pH ofthe water at ambient temperature is in the region of 6.5 to 7.5, and athigher operating temperatures is lower, generally in the region of about5.5-5.8, for example 5.65. (This is due to increased dissociation of thewater at the higher temperatures.) In addition, an operating BWR hasvery stringent coolant water conductivity levels which must be observed.Typically, the conductivity of the coolant water must not exceed 0.3FS/cm, and more usually must be less than 0.1 FS/cm. Such conductivitylevels are adversely impacted by high concentrations of ionic species,and effort is made in the NobleChem™ to ensure that reactor ionicconcentrations are maintained as low as possible after clean-up,preferably less than 5 ppb. For example, the process in particularexcludes the use of chloride ion in view of its corrosive nature.

While not being bound by theory, it is understood that the metal, forexample platinum and/rhodium, is incorporated into the stainless steeloxide film via a thermal decomposition process of the compound whereinmetal ions/atoms apparently replace iron, nickel and/or chromium atomsin the oxide film, resulting in a metal-doped oxide film. The metal,such as platinum/rhodium, may for example be incorporated within or onthe surface of the oxide film and may be in the form of a finely dividedmetal. The oxide film is believed to include mixed nickel, iron andchromium oxides.

Following injection and incorporation of the metal(s) in the oxidizedstainless steel surfaces, the water is subjected to a conventionalclean-up process to remove ionic materials such as nitrate ions presentin the water. This clean-up process is usually carried out by passing afraction of the water removed from the bottom head of the reactor andrecirculation piping through an ion exchange resin bed, and the treatedwater is then returned to the reactor via the feedwater system. Hydrogenmay subsequently be introduced into the water some time after the dopingreaction, for example 1 to 72 hours after injection and incorporation ofthe metal atoms in the oxidized surface, to catalyze recombination ofhydrogen and oxygen on the metal doped surfaces. As hydrogen is added,the potential of the metal-doped oxide film on the stainless steelcomponents is reduced to values which are, much more negative than whenhydrogen is injected into a BWR having stainless steel components whichare not doped with the noble metal.

The NobleChem™ process, as basically and briefly outlined above, offersthe advantage that steel surfaces within a water-cooled reactor can bedoped with noble metal using an in situ technique (i.e., while thereactor is operating) that is simple in application and alsoinexpensive. Moreover, the process can also be applied to both operatingBWRs and PWRs. However, during the NobleChem™ process or any similar insitu metal deposition process, it is necessary to make certain informeddecisions concerning how and when to modify various reactor operatingconditions—such as water temperature and noble metal-containing compoundinjection rate—to maintain proper metal loading throughout thedeposition process.

Conventionally, the only way to obtain information on the state of adynamic fluid system has been to perform simple non-steady state massbalances on the fluid within the system. Unfortunately, the procuring ofa simple mass balance has proved inadequate for accurately assessing thestate of metal deposition and controlling metal loading during in situreactor deposition processes such as the above described NobleChem™process—due at least in part to the non-uniformity of metal depositionthat typically occurs throughout the water flow circuit in a reactor inaddition to other logistical factors inherent to the in situ process andenvironment as a whole.

BRIEF SUMMARY OF THE INVENTION

The present invention relates to both a method and system for modelingand maintaining the amount of noble metals deposited in the water flowcircuit of a boiling water reactor during an in situ noble metalapplication process, such as the NobleChem™ process described above. Anon-steady state computer model of the water in a Boiling Water Reactor(BWR) primary water flow circuit, and other piping directly connected toit, is used to represent the water chemistry and the noble metal loadingthat occurs before, during and after the noble metal applicationprocess. The modeling program tracks the noble metal application processvia computed simulation based on reactor conditions and water samples(also called “coupons”) taken, for example, at various locationsthroughout the flow circuit every few hours or so. Such testing of theflow circuit water may be performed during the metal application processwhile the reactor is operating, for example, in a “hot standby” mode.

In an example embodiment of the present invention, a software system formodeling water in a BWR is provided as an application/utility for use ona computer system having an associated display device and/or otheroutput device for producing graphs and charts (e.g., a PDA, laptop,etc.). The software program code for the noble metal deposition modelingmethod of the present invention may be embodied in any computer-readablemedium for loading and executing on a computer system. Preferably, themodeling software of the present invention is provided on a laptop orportable computer to enhance its transportability for use at differentreactor sites. An Exel™ spreadsheet program is used to create a workbookof spreadsheets containing power plant system data for modeling reactorwater circuit flow that include geometric configuration data, pertinentoperational parameters, simulation parameters, chemical parameters andinitial water chemistry data. Alternatively, a portable electronicdigital communications device having access via a wireless or landlinedigital communications link such as, for example, the Internet to aremote computer that performs the noble metal deposition modeling asdescribed herein is also contemplated by the present invention.

The following description is directed toward a presently preferredembodiment of the present invention, which may be operative as anend-user application running, for example, under the Microsoft® Windows95/NT environment. The present invention, however, is not limited to anyparticular computer system or any particular environment. Instead, thoseskilled in the art will find that the system and methods of the presentinvention may be implemented using almost any contemporary conventionalpersonal or desktop computer system or computer network. Moreover, theinvention may be embodied on a variety of different platforms, includingUNIX, LINUX, Macintosh, Next Step, Open VMS, and the like. Therefore,the description of the exemplary embodiments which follows is forpurposes of illustration and not limitation.

Information and system data characterizing a particular reactor plantmay be placed, for example, on a magnetic disk (or other portablestorage device) in the form of comma delimited text files. After thedata representing the initial state of the reactor water chemistry andinitial operating conditions of the reactor is read and input into theappropriate spreadsheet file, the modeling software determines the waterchemistry, pH, conductivity and noble metal loading through the BWRprimary water flow circuit, including selected sampling locations, as afunction of time. The results are saved in files and displayed as chartsor graphs for ascertaining whether technical specifications onconductivity or other water chemistry-related parameters will beexceeded during the noble metal application process.

In addition, the values of rate constants used for modeling the noblemetal reactions can be changed on site at the reactor during an ongoingin situ application process and the modeling routine re-run until thenumerical results from the computer model become consistent with actualmeasured concentrations of noble metals at selected sample locations. Inthis manner, a “best estimate” of the noble metal loading occurringwithin the BWR water flow circuit is obtained and the operatingconditions of the reactor can then be immediately changed if thecalculated loading rates are inconsistent with predetermined targetgoals.

In an example embodiment of the metal deposition process modeling aspectof the present invention, each region of the reactor water flow circuitis characterized as being comprised of smaller “cells” of equal flowresidence time. In this manner, non-steady state mass balances can bemaintained where parallel flow regions merge despite unequal flowresidence times in each region. Mass balances are performed on all cellsto account for transport-in, transport-out and chemical reactions. Theconcentrations of all relevant ionic species (including Cl⁻, Na⁺, NO₂ ⁻,NO₃ ⁻, SO₄ ⁻, ZnOH, Pt(OH)₆ ⁻⁻, Rh(NO₂)₆ ⁻⁻⁻, OH⁻, H⁺) are determinedbased upon the initial concentrations in the flow circuit, measuredconcentrations in inlet and outlet streams, reactor water clean-upefficiency and local reaction rates. The cumulative concentrations ofall the ionic species are then used to determine pH and conductivity.Reaction rates are also determined both for bulk processes (such as thedecomposition of noble metal complexes due to thermal decomposition,radiation and other chemicals) and the reactions of chemical specieswith the metal surfaces in the flow circuit, including the deposition ofnoble metal with the simultaneous formation of OH⁻ or NO₂ ⁻. Thesesurface reaction rates are used for determining noble metal accumulationrates and consequent accumulated noble metal concentrations on thesurfaces throughout the circuit.

In the disclosed example embodiment, the noble metal application processmodeling routine of the present invention is complemented withconventional macro routines for generating and displaying prescribedgraphs from initial data and for importing new data developed from each“run” (i.e., execution of the process modeling software) so thatselected graphs may be re-plotted as desired. For example, a macroroutine is provided for importing data from a modeling run into anExcel™ workbook containing forms for generating prescribed graphs ofinterest. Likewise, another macro routine is provided for linking anExcel™ workbook containing a graph to a previously generated set ofgraphs.

The modeling method of the present invention is also useful inperforming non-steady state evaluations of water chemistry transients inBWRs. For example, concentrations of water impurities in a BWR due toleaking fuel rods, corroding components or other intrusions can beeasily modeled by including “source” terms in the modeling routine torepresent an impurities at probable locations that might account fortheir appearance. Likewise, the disappearance of various impurities, forexample, due to incorporation into crud or radioactive decay, can beaccounted for by including representative “sink” terms in the modelingroutine. In this manner, the non-steady state concentration ofradioactive isotopes, corrosion products and water impurities could bedetermined for the entire water flow circuit(s) throughout the reactorand in the steam for performing, for example, analysis on fuel leaks andcorrosion.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic showing a partially cutaway perspective view of aconventional BWR;

FIG. 2 is a diagram illustrating an example system including a blockdiagram illustrating the use of a portable processing arrangement forutilizing the modeling software of present invention;

FIG. 3 is a flow diagram illustrating an exemplary method forimplementing the present invention;

FIG. 4 is a diagram illustrating an example of the general proceduralsteps for using the noble metal application process modeling software ofthe present invention; and

FIGS. 5A-5E illustrate an exemplary program flow diagram for the metalapplication process modeling software of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The fluid flow in a boiling water reactor (BWR) will be generallydescribed with reference to FIG. 1. Feed-water is admitted into areactor pressure vessel (RPV) 10 via a feed-water inlet 12 and afeed-water sparger 14, which is a ring-shaped pipe having suitableapertures for circumferentially distributing the feed-water inside theRPV. A core spray inlet 11 supplies water to a core spray sparger 15 viacore spray line 13. The feed-water from feed-water sparger 14 flowsdownwardly through the downcomer annulus 16, which is an annular regionbetween RPV 10 and core shroud 18. Core shroud 18 is a stainless steelcylinder which surrounds the core 20 comprising numerous fuel assemblies22 (only two 2×2 arrays of which are depicted in FIG. 1). Each fuelassembly is supported at the top by top guide 19 and at the bottom bycore plate 21. Water flowing through downcomer annulus 16 then flows tothe core lower plenum 24.

The water subsequently enters the fuel assemblies 22 disposed withincore 20, wherein a boiling boundary layer (not shown) is established. Amixture of water and steam enters core upper plenum 26 under shroud head28. Core upper plenum 26 provides standoff between the steam-watermixture exiting core 20 and entering vertical standpipes 30, which aredisposed atop shroud head 28 and in fluid communication with core upperplenum 26.

The steam-water mixture flows through standpipes 30 and enters steamseparators 32, which are of the axial-flow centrifugal type. Theseparated liquid water then mixes with feed-water in the mixing plenum33, which mixture then returns to the core via the downcomer annulus.The steam passes through steam dryers 34 and enters steam dome 36. Thesteam is withdrawn from the RPV via steam outlet 38.

The BWR also includes a coolant recirculation system which provides theforced convection flow through the core necessary to attain the requiredpower density. A portion of the water is sucked from the lower end ofthe downcomer annulus 16 via recirculation water outlet 43 and forced bya centrifugal recirculation pump (not shown) into jet pump assemblies 42(only one of which is shown) via recirculation water inlets 45. The BWRhas two recirculation pumps, each of which provides the driving flow fora plurality of jet pump assemblies. The pressurized driving water issupplied to each jet pump nozzle 44 via an inlet riser 47, an elbow 48and an inlet mixer 46 in flow sequence. A typical BWR may have sixteento twenty-four inlet mixers.

During an in situ noble metal application process for a BWR, it isperhaps most useful to know of the degree of noble metal loading as afunction of location along water flow paths within the BWR.Consequently, in the method of the present invention, distinct regionsof water flow are subdivided into multiple cells for modeling andanalysis. In addition, since mass balances must be maintained whereverparallel flow regions merge despite unequal flow residence times withinthe region, the modeling routine of the present invention selects cellshaving equal flow time.

Referring now to FIG. 2, an example portable computing system 100 forutilizing the modeling software of present invention is shown along witha block diagram below it illustrating the general input/outputprocessing flow of information. For example, text files 101 containinginitialization parameters and other data may be created (or input froman alternate source) on a portable processor 102 using conventionalprogramming applications such as Excel.™ After the noble metal loadingsimulation/modeling program of the present invention is run, an ASCIoutput file 103 containing computed model data is produced fordisplaying charts/graphs 104 of the modeled noble metal loading.

FIG. 3 shows a flow diagram 110 that illustrates exemplary steps thepresent method for evaluating and maintaining the proper noble metalloading during an in situ noble metal application process such asmentioned above. Each box of the diagram of FIG. 3 contains a conciseexplanation of a particular step for this example embodiment of themethod of the present invention. As indicated at block 112, the initialstate of reactor water chemistry and initial operating conditions areinput by a user on a processing system (100) containing the modelingprogram of the present invention. The modeling program is then run whichcomputes, at block 114, noble metal loading throughout the flow circuit,specifications for conductivity and other parameters based on the inputparameters. The user then proceeds to obtain samples of noble metalconcentrations at various locations throughout the water-flow circuitwithin the reactor, as indicated at block 116. The actual measuredconcentrations from the acquired samples can then be compared to thecomputed model results for corresponding locations and may be used toalter particular rate-constants employed by the modeling program, asindicated at block 118, until the modeling program output agrees withthe actual measured concentrations. Once the modeling program iseffectively “calibrated” in this manner, it may then may be run again atvarious times during the application process, as indicated at block 120,to provide an immediate best estimate of noble metal loading for anydesired location within the reactor water-flow circuit.

If the computed best estimate of noble metal loading is consistent withpredetermined target goals for the noble metal application process(block 122), further samples may be taken at later times (block 124) tocontinue the evaluation process or, alternatively, the evaluation may beterminated (block 128). After the above “calibration” of the modelingprogram (block 118) has been achieved, if a subsequent computed bestestimate of noble metal loading (block 120) is not consistent with thetargeted goals of the NobleChem™ process for the reactor (block 122),then such divergence(s) may serve as an indication that the operatingconditions of the reactor may need to be at least temporarily altered(block 126). For example, the noble metals in the water flow circuit canbe altered by producing a change in the rate-constant effected bychanging the current operational criteria/conditions of the reactor.

FIG. 4 covers some example general procedural steps which may befollowed for using the simulation/modeling software of the presentinvention. Referring now to FIG. 4, steps 202 through 210 illustrateexample steps performed before the noble metal deposition processsimulation/modeling routine is launched. For example, the user/operatormay begin by opening the workbook application for running the modelingprogram installed on a portable (or other) computer (block 202). Theuser/operator then inputs simulation parameters for the processincluding, for example, initial concentrations, reactor operatingparameters, and chemical parameters and rate constants for theparticular reactor and the noble metal application process (block 204).Next, the user/operator runs a set-up macro for the noble metal loadingsimulation/modeling program (block 206). This is a simple set-up macrothat has been created to produce a text file of predetermined formatcontaining labels and values for various input parameters and reactorspecific geometric parameters, which may be provided, for example, fromreactor-specific spreadsheet data stored within the same computer (block208). The macro then launches the executable modeling program (block210) stored on the same computer for performing the noble metal loadingcomputations and analysis, the results of which may be locally displayedfor immediate review.

Basically, the modeling method implemented by the noble metalapplication process simulation program of the present inventionintegrates kinetic flow equations in a non-steady state system comprisedof individual fluid-slug flow regions and sub-regions within thereactor. Some of these flow regions are considered as coupled andflowing in series, and some in parallel. This approach can be appliedusing conventional kinetic equations, because it basically models a setof mass balances in series—although a somewhat more basic linearmodeling embodiment is preferred as a reasonable and easily implementedapproximation to actual reactor conditions. If desired, more detailedand non-linear fluid kinetics may be assumed and used to more accuratelymodel conditions within particular reactors. The specific rate constantsreferred to in the following discussion of applicable kinetic data mayalso be altered accordingly, as determined by empirical data.

Kinetic Equations

The basic equations for determining loading and decomposition are asfollows:

d(c)/dt=−(k _(s) +k _(t) +k _(z) +k _(r))c (rate of destruction of noblemetal compound)

d(s)/dt=k _(s) c(D _(h)/4) (rate of surface loading of noble metalcompound)

d(d)/dt=−(k _(t) +k _(z) +k _(r))c (rate of creation of inactive noblemetal species)

where:

c=concentration of noble metal for the injected compound, g (or g moles)metal/unit volume

d=concentration of metal for the deactivated compound, g (or g-moles)metal/unit volume

s=surface concentration of noble metal, g (or g-moles) metal/unit area

As knowledge of the noble metal kinetics improves, one of ordinary skillwill appreciate that it may become necessary to make this example modelmore complex. For example, although it is not commonly known whetherdeactivation is actually heterogeneous (occurring at surfaces) orhomogeneous, it is assumed to be homogeneous in the example embodimentdisclosed herein. Particles of deactivated noble metal may collide withthe surface, and deposit some otherwise deactivated noble metal.Particles of deactivated noble metal or crud may also be responsible fordeactivation. If so, then one must account for the particle sizedistribution. In any event, the framework of the model presented hereinshould work with any kinetics.

In the example embodiment herein, it is assumed that all reaction rateconstants may be represented by the Arrhenius formula as follows:

k _(s) =A _(s)(4/D _(h))exp[−B _(s) /RT] surface

k _(t) =A _(t) exp[−B _(t) /RT] thermal

k _(z) =A _(z) Zn exp[−B_(z) /RT] zinc

 k _(r) =A _(r) G exp[−B _(r) /RT] radiation

where:

D_(h) is the hydraulic diameter

Zn is the zinc concentration

G is the gamma dose rate.

The overall rate constant is defined by:

k _(o)=(A _(s)(4/D _(h))exp[−B _(s) /RT]+A _(t) exp[−B _(t) /RT]+A _(z)Zn exp[−B _(z) /RT]+A _(r) G exp[−B _(r) /RT])

so that

d(c)/dt=−k _(o) c

Example General Modeling Approach

The approach of the present invention in applying the above equations isto divide each flow region and sub-region of the reactor intosub-lengths such that the residence time of every sub-length is Δt. Thismakes it straight-forward to analyze any fluid element using a totaltime derivative. In this way, it is possible to follow individual“slugs” of water as they flow from one sub-length to the next. Also,using this approach, it is possible to add parallel streams together andensure that a true mass balance is maintained. Example regions andsub-regions of the reactor are defined a list provided at the end ofthis discussion. For this example, Δt should equal 1 second, althoughthe user can elect to select a different value. However, selecting amuch larger value for Δt would result in bypassing the sub-regions ofshortest residence time, which should be avoided.

Each sub-region of the primary system is characterized by the followingprimary quantities:

Length (L)

Surface area (S)

Volume (V)

Flow rate (Q)

The water flow velocity in a sub-region is given by:

v=QL/ρV

In a given region, the sub-length is given by:

ΔL=Δtv=ΔtQLρV

The number of sub-lengths in a region is given by:

n=L/ΔL

In practice, n is rounded up to the next nearest integer. Because ofthis rounding, the formulation only represents the geometryapproximately. However, this should only have a small effect on theresults. The effect is minor compared with some of the assumptions inthe model, such as the use of simple rate expressions and kinetics, theneglect of any influence of crud, and the use of plug flow in allregions.

At time mΔt, each sub-length in each region is characterized by valuesof c, d, and s. In most cases, these will be set equal to 0 when timeequals 0. However, non-zero values may also be used at time 0, dependingon the application.

Suppose the sub-lengths of a region are numbered from 1 to n. For thegeneral interior sub-length i, with concentrations c(i, mΔt), d(i, mΔt),and s(i, mΔt) at time mΔt, the concentrations at time (m+1)Δt are givenby

c(i, (m+1)Δt)=c(i−1, mΔt)−k _(o) c(i−1, mΔt)Δt

d(i, (m+1)Δt)=d(i−1, mΔt)+(k _(t) +k _(z) +k _(r))c(i−1, mΔt)Δt

s(i, (m+1)Δt)=s(i, mΔt)+(D _(h)/4)k _(s) c(i, mΔt)

An equation similar to the equation for c can be used for other speciesin the water, with appropriate modification of the rate constants toaccount for stoichiometry. For example, OH⁺ ions are generated by thedecomposition of Pt(OH)₆ ⁻ ions. The equation of change of OH⁻ is:

OH⁻(i, (m+1)Δt))=OH⁻(i−1, mΔt)+6f _(OH−) k _(o,Pt) c _(Pt) _(—)_(complex)(i−1, mΔt)Δt

where c is on a molar basis, and f_(OH−) is the fraction of the OHgroups converted to ions.

Similarly, the equation for change of NO₂ ⁻ due to the decomposition ofRh(NO₂)₆ ⁺⁺⁺ is

NO₂ ⁻(i, (m+1)Δt))=NO₂ ⁻(i−1, mΔt)+6k _(o,Rh) c _(Rh) _(—)_(complex)(i−1, mΔt)Δt

where the process is assumed to be 100% efficient.

Region Entrance Conditions

In addition to the general interior sub-lengths, the inlet and outletconditions for each region, corresponding to the first and lastsub-lengths of a region, are specified. For simplicity, any inlet flowor outlet flows will occur between the last sub-length of a sub-regionand the first sub-length of the next sub-region.

Consider the beginning of a sub-region receiving flows Q₁, Q₂, and Q₃,with active concentrations c₁, c₂, and c₃ and deactivated concentrationsd₁, d₂, and d from three separate sources (this is the maximum I believerequired for this system). The flows may either be from othersub-regions leading into the sub-region or inlet flows to the system.For example, at the entrance to the upper plenum, Q₁ is the fuel channelflow, Q₂ is the core bypass flow, and Q₃ is the outer bypass flow.

The flow rate for the new sub-region is

Q=Q ₁ +Q ₂ +Q ₃

the active concentration is

 c=(Q ₁ c ₁ +Q ₂ c ₂ +Q ₃ c ₃)/Q

and the inactive concentration is

d=(Q ₁ d ₁ +Q ₂ d ₂ +Q ₃ d ₃)/Q

The same set of equations may be used if there is an outlet stream. Forthe outlet stream, the sign of Q is negative.

Example Specifications for Pt and Rh Process

Example species that are tracked in the flow water are shown below inTable 1.

TABLE 1 Species whose concentrations are tracked by the model SpeciesConcentration label Cl⁻ CLM H⁺ HP H2O H2O Na⁺ NAP Pt(OH)₆ ⁻⁻ PTOH6MMRh(NO₂)₆ ⁺⁺⁺ RHNO26MMM NH₃ NH3 NO₂ ⁻ NO2M NO₃ ⁻ NO3M OH⁻ OHM Pt(deactivated form) PT_DEACT Rh (deactivated form) RH_DEACT SO₄ ⁻⁻ SO4MMZn ZN ZnOH⁺ ZNOHP

In the present example, in addition to the above listed components,surface-loaded concentrations of Pt and Rh are also tracked. The labelsused for such are PT_SURF and RH_SURF, respectively.

The concentrations of chemical species are calculated by mass balancethroughout the reactor. The only species of interest that is notcalculated by mass balance is zinc. This is because: 1) zinc appears toreach an equilibrium value, unaffected by the parameters of the model;2) we do not currently have a method to calculate zinc concentrations;and 3) zinc is only used in order to predict the conductivity.Initially, the zinc concentration will only be measured and input (aslisted in Table 6). If there is supporting data, the zinc concentrationmay later be used in the calculation of k_(z).

Table 2 shown immediately below lists example chemical parameters usedby the modeling program of the present invention. These are parametersused to 1) calculate the rate of change of the active chemicals, 2)calculate conductivity, 3) calculate pH.

TABLE 2 Chemical parameters Chemical parameter Label Bulk decompositionrate constant for KB_PT Na₂Pt(OH)₆ Bulk decomposition rate constant forKB_RH Na₃Rh(NO₂)₆ Equivalent conductance of active Pt(OH)₆ COND_PTOH6MMEquivalent conductance of active Rh(NO₂)₆ COND_RHNO26MMM Equivalentconductance of CF COND_CLM Equivalent conductance of H⁺ COND_HPEquivalent conductance of Na⁺ COND_NAP Equivalent conductance of NO₂ ⁻COND_NO2M Equivalent conductance of NO₃ ⁻ COND_NO3M Equivalentconductance of OH⁻ COND_OHM Equivalent conductance of SO₄ ⁻⁻ COND_SO4MMEquivalent conductance of ZnOH⁺ COND_ZNOHP Fraction of OH given off asOH from Pt(OH)₆ FROHM decomp. Ion-constant product for H2O KW Ionizationconstant for Zn KI_ZN Radiation-induced decomp. rate constant for KR_PTNa₂Pt(OH)₆ Radiation-induced decomp. rate constant for KR_RH Na₃Rh(NO₂)₆Surface loading rate constant for Na₂Pt(OH)₆ KS_PT Surface loading rateconstant for Na₃Rh(NO₂)₆ KS_RH

Numerical values for flow lengths, volumes, and surface areas areprovided by the user for each of the reactor regions. Table 3 belowprovides a list of labels used to define these quantities in the examplemodeling program. The corresponding values are provided by the user(e.g., determined externally and provided to the modeling program). Inthis example, provisions are made for using up to three segments persample line with differing geometry, but constant mass flow rate. Inaddition to the primary circuit, two sample lines are included.

TABLE 3 Length, surface, and volume labels Surface Length area VolumeSub-region label label Label Fuel channel LFUEL SFUEL VFUEL Region Hfuel channel LFUELH SFUELH VFUELH Core bypass, g LCORBYP SCORBYP VCORBYPRegion H bypass LCORBYPH SCORBYPH VCORBYPH Outer bypass LOBYP SOBYPVOBYP Region H outer bypass LOBYPH SOBYPH VOBYPH Upper plenum LUPLENSUPLEN VUPLEN Steam separator region 1 LSS1 SSS1 VSS1 Steam separatorregion 2 LSS2 SSS2 VSS2 Steam separator region 3 LSS3 SSS3 VSS3 Steamseparator region 4 LSS4 SSS4 VSS4 Steam separator region 5 LSS5 SSS5VSS5 Steam separator region 6 LSS6 SSS6 VSS6 Mixing plenum, above LMPASMPA VMPA feedwater mix Mixing plenum, below LMPB SMPB VMPB feedwatermix Downcomer, s1 start LD1 SD1 VD1 Downcomer, s1 carry under LD2 SD2VD2 Downcomer, s2 + s31 LD3 SD3 VD3 Downcomer, s32 + s4 + s5 LD4 SD4 VD4Recirc suction pipe LR1 SR1 VR1 Recirc discharge pipe LR2 SR2 VR2 Recircheader ring LR3 SR3 VR3 Recirc riser pipe LR4 SR4 VR4 Recirc jet pumpinternal LR5 SR5 VR5 riser Recirc jet pump nozzle LR6 SR6 VR6 (ramshead) Jetpump, throat LJP1 SJP1 VJP1 Jet pump, diffuser LJP2 SJP2 VJP2Jet pump, tailpiece LJP3 SJP3 VJP3 Lower plenum, down-flow LLP1 SLP1VLP1 Lower plenum, up-flow LLP2 SLP2 VLP2 below core plate Lower plenum,up-flow LLP3 SLP3 VLP3 above core plate Sample line A, 1st sectionLSAMPA1 SSAMPA1 VSAMPA1 Sample line A, 2nd section LSAMPA2 SSAMPA2VSAMPA2 Sample line A, 3rd section LSAMPA3 SSAMPA3 VSAMPA3 Sample lineB, 1st section LSAMPB1 SSAMPB1 VSAMPB1 Sample line B, 2nd sectionLSAMPB2 SSAMPB2 VSAMPB2 Sample line B, 3rd section LSAMPB3 SSAMPB3VSAMPB3

For the present example, Table 4 immediately below illustrates someadditional reactor design parameters which the user may need to provide.

TABLE 4 Additional reactor design parameters Design parameter LabelFraction of bypass flow moving through outer FROUTER bypass Fraction ofcore flow moving through jet pumps FRJETP Fraction of flow exiting steamseparator region 3 FRSS3 Fraction of core flow moving through fuelFRCHAN channels Number of fuel bundles NBUNDLE Number of jet pumpsJPNUMBER Number of steam separators SEPNUM

Table 5 below shows example definitions and entrance conditions used foreach sub-region. For each sub-region, the volume, length, andsurface-to-volume ratio (which equals 4/D_(h)) are provided by the user.

TABLE 5 Flows in primary loop (TF = total flow) Flow Q EntranceSub-region Label (kg/s) streams Fuel channel QFUEL TF*FRCHAN/ LP3NBUNDLE Region H fuel QFUELH TF*FRCHAN/ FUEL channel NBUNDLE Corebypass, g QCORBYP TF*(1-FRCHAN)* LP3 (1-FROUTER) Region H bypassQCORBYPH TF*(1-FRCHAN)* CORBYP (1-FROUTER) Outer bypass QOBYPTF*(1-FRCHAN)* LP3 FROUTER Region H outer QOBYPH TF*(1-FRCHAN)* OBYPbypass FROUTER Upper plenum QUPLEN TF FUELH CORBYPH OBYPH Steamseparator QSS1 TF/SEPNUM UPLEN region 1 Steam separator QSS2 TF/SEPNUMSS1 region 2 Steam separator QSS3 TF/SEPNUM* SS2 region 3 FRSS3 Steamseparator QSS4 TF/SEPNUM* SS2 region 4 (1-FRSS3) Steam separator QSS5TF/SEPNUM* SS4 region 5 (1-FRSS3) Steam separator QSS6 O region 6 Mixingplenum, QMPA TF SS3 above fw mix SS5 Mixing plenum, QMPB TF MPA below fwmix Downcomer, s1 start QD1 TF MPB Downcomer, s1 QD2 TF D1 carry underDowncomer, s2 + QD3 TF D2 s31 Downcomer, s32 + QD4 TF*(1-FRJETP) D3 s4 +s5 Recirc suction pipe QR1 TF*(1-FRJETP)/2 D4 Recirc discharge QR2TF*(1-FRJETP)/2 R1 pipe Recirc header ring QR3 TF*(1-FRJETP)/2 R2 Recircriser pipe QR4 2*TF*(1-FRJETP)/ R3 JPNUMBER Recirc j.p. internal QR52*TF*(1-FRJETP)/ R4 riser JPNUMBER Recirc j.p. nozzle QR62*TF*(1-FRJETP)/ R5 (rams head) JPNUMBER Jet pump, throat QJP1TF/JPNUMBER D3 R6 Jet pump, diffuser QJP2 TF/JPNUMBER JP1 Jet pump,tailpiece QJP3 TF/JPNUMBER JP2 L.P., down-flow QLP1 TF JP3 L.P., up-flowbelow QLP2 TF QLP1 c.p. L.P., up-flow above QLP3 TF QLP2 c.p. Sampleline A, 1st QSAMPA1 QSAMPA EXITA section Sample line A, 2nd QSAMPA2QSAMPA SAMPA1 section Sample line A, 3rd QSAMPA3 QSAMPA SAMPA2 sectionSample line B, 1st QSAMPB1 QSAMPB EXITB section Sample line B, 2ndQSAMPB2 QSAMPB SAMPB1 section Sample line B, 3rd QSAMPB3 QSAMPB SAMPB2section

In, for example, the NobleChem™ metal application process, the streamsentering the loop (chemical injection, feedwater cleanup, control rod)and exiting the loop (sample line, recirculation to RWCU, drain line toRWCU) are extremely small compared with the core flow. None of theseflows will significantly affect the velocity. Only the injection flowwill significantly affect any local concentrations. The effects of theother streams on concentration, while ultimately important, arerelatively slow and non-localized. Therefore, they can be lumpedtogether. This is a useful simplification, in that it prevents theaccumulation of numerical round-off errors. It is assumed that there areonly two inlet flows (chemical injection and feedwater cleanup) andthree outlets (RWCU from recirculation loop, and two sample lines). Thecontrol rod drive flow will be assumed to equal 0, and the feedwatercleanup flow rate assumed to equal the sum of the RWCU and sample lineflow rates minus the injection stream flow rate.

The total flow (TF) in the primary system varies as water enters andexits. TF equals CF from the middle of the mixing plenum until the nextentrance or exit stream. TF decreases by QSAMPA at the recirculationdischarge. TF increases by QIS, the injection stream flow rate, at therecirculation header. TF decreases by QRWCU at the RWCU take-off point,assumed to be the bottom of the lower plenum. TF decreases by QSAMPB atcore plate. Finally, TF increases by the amount(QRWCU+QSAMPA+QSAMPB−QIS) in the middle of the mixing plenum.

Table 6 shown immediately below lists example parameters to be input bythe user. These values may be changed by the user. For example, the usermay elect to change various chemical parameters in response to samplemeasurements taken in order to improve the match of the computed modelto the actual NobleChem™ process. The operating parameters may beentered in steps. For this example, at least fifty of such steps arepermitted.

TABLE 6 Example Operating parameters to be input by the user: Operatingparameter Label Core flow rate (kg/h) CF Injection stream flow rate(kg/h) QIS Na₂Pt(OH)₆ inlet flow rate (g metal/h) PTIN Na₃Rh(NO₂)₆ inletflow rate (g metal/h) RHIN Nitric acid inlet flow rate (moles/h) HNO3RWCU efficiency (%) EFFRWCU RWCU flow rate (kg/h) QRWCU Sample line Aflow rate (kg/h) QSAMPA Sample line B flow rate (kg/h) QSAMPB Sodiumhydroxide inlet flow rate (moles/h) NAOH Temperature of water in reactor(degrees C.) TEMPC Thermal power at shutdown (MW) THERM Time betweenshutdown and beginning of TIMEDELAY simulation Water level (m) WL Zinc(total) in water (ppb) ZN

Table 7 shown immediately below summarizes some example intermediateparameters. These are values that are used by the model, and which willbe not altered by the user. The average core dose rate is calculated asa function of the thermal power at shutdown and the time betweenshutdown and the beginning of the simulation. The water density iscalculated as a function of temperature, and will change from itsinitial value if the temperature changes.

TABLE 7 Intermediate parameters Intermediate parameter Label Averagecore gamma dose rate GAMMA (MRad/hr) Water density (kg/m³) DENS

Example Simulation Program

FIGS. 5A-5E are flow diagrams illustrating example functional stepsperformed by the executable noble metal application modeling routine ofthe present invention. One of ordinary skill will appreciate that suchsteps may be implemented on any particular computer by utilizingconventional programming techniques and programming tools well known inthe art.

Referring now to FIG. 5A, blocks 310 to 320 illustrate example steps forinitializing the modeling computations. For example, a text filepreviously created by the user (see FIG. 4) defines the noble metalapplication process variables to be analyzed (block 310). Input valuesare obtained from the text file (blocks 312 and 314) and converted tomodel units (block 316). Intermediate parameters are then computed(block 318) and set up to prepare for the modeling/simulation run (320)as further described with respect to FIG. 5B.

Referring now to FIG. 5B, blocks 410 through 434 illustrate examplesteps for preparing and computing internal parameters used in theprocess modeling/simulation. For example, times and core dose rates(e.g., gamma vs. time for base case reactor) for standard shutdowncondition are defined (block 410). Relative power density at shutdown(compared to base case) is determined (block 412). Minimum core flow forall input steps is computed to determine the required number of cells(block 414). Flow rates (of all regions) at minimum core flow rate arecomputed to determine the number of cells (block 416). Region flowsduring operating step of minimum flow are determined (block 418). Thecell Delta Length is computed for each region (block 420). The number ofcells in each region is computed (block 422). Indexes for the first cellin each sub-region are determined (block 424) and the total number ofcells is then determined (block 426). Next, indexes for inlet streamsare defined (block 428) and arrays for tracking concentrations arecreated and initialized (block 430), converting values from ppb (asinput) to moles/liter. Next, the concentrations of unidentified ions arecomputed based on initial measured pH and noble metals (block 432) andlabels and indexes are set up for output (434).

Referring next to FIG. 5C, blocks 436 through 456 illustrate examplesteps for performing computations for determining concentrations ofchemicals and noble metal loading rates. For example, computations areperformed for determining variable/parameter values; and variablesrepresenting time, Pt and Rh material balance components are initialized(block 436). At this point, operating variables (e.g., flow rates,temperatures, RWCU efficiency, injection rates) may be updated if thenext operating time interval is reached (block 438). Next, operatingvariables are converted to MKS units (block 440), region flows aredetermined (in m³/s) for the current operating time interval (block442), the values of the time step and number of time steps in thecurrent operating interval are determined (block 446), and feedwaterinlet concentrations based on RWCU efficiency are computed (block 448).The individual operating time interval computations are then performed,for example, using a For/next loop (block 450). The current time isupdated (block 452) and results for each sub-region during the currenttime-step are computed (block 454). Next, a sub-region is selected(block 456).

Referring now to FIG. 5D, entrance flow rates and labels of entrancestreams are defined (block 458). The number of cells, first index,velocity, hydraulic diameter, surface-to-volume ratio, volume andtemperature are also defined (block 458). Next, the rate constants foeall bulk and surface chemical reactions are updated based on currentlocal gamma dose rate, geometry, velocity and temperature (block 460).Entrance concentrations for the sub-region are determined based on inletstreams concentrations in the previous operating time interval (block462). Next, new concentrations and loadings of the first cell of thesub-region are computed using chemical kinetic equations based on localrate constants and bulk concentrations at the entrance (block 464). Forthe remaining cell concentrations in the sub-region, temperature in thecell is determined if the temperature varies within the region (block468) and if local temperature is re-determined, the rate constants arealso re-determined (block 470), and new concentrations and surfaceloadings in the cell are computed using chemical kinetic equations basedon local rate constants and concentrations of the previous cell in theprevious operating time interval (block 472). At this point, the stepsin blocks 468 through 472 are performed again for each cell in thesub-region currently being evaluated until all cells in the sub-regionhave been evaluated (block 474). Next, the concentration arrays for theoperating time interval for each cell of each sub-region and thematerial balances for Pt and Rh are updated (block 476 and block 478).

Referring now to FIG. 5E, blocks 480 through 508 illustrate examplesteps for assembling selected computed modeling/simulation results foroutput. Next, the current time is checked to determine if an outputshould be generated (block 480) in accordance with some user-selectedpredetermined output interval. For example, printing or displaying modelresults may be scheduled for every x minutes. If the current time isgreater than the next scheduled output time, then for selected locations(block 482) the following steps are performed (blocks 484 through 492):H+ and OH− concentrations are selected based either on: 1) chargebalance with other ions and initial unidentified ion concentration or 2)H+ and OH− concentrations are determined via chemical reactions (block484); the pH is computed using H+ (block 486); the water conductivity isthen computed based on all ions and their respective conductance (block488); the state of the system (i.e., ion concentrations, loading, pH,conductivity, etc.) is output for the selected locations (block 490);and the next print time is then updated (block 492), after whichprocessing continues with determining if more time steps remain in thecurrent operating interval (block 494). Referring back to block 480 inFIG. 5E, if the current time is earlier than the next scheduled outputtime, then processing continues with determining if more time stepsremain in the current operating interval (block 494).

If there more time steps remain within the current operating interval,the current time is updated (block 452 in FIG. 5C) and themodeling/simulation continues for another sub-region (block 454 in FIG.5C). If there are no more time steps within the current operatinginterval (block 494), it is then determined if further operating timeintervals remain to be evaluated (block 496). If further operatingintervals are to be modeled, the processing continues with updating theoperating variables for the next operating time interval (operatingstep), as indicated at block 438 (FIG. 5C). If no further operatingintervals are to be processed, the simulation is essentially complete(block 498) and the final state data (i.e., ion concentrations,loadings, pH, and conductivity for all cells) may be output via printeror display (500).

In the above described example, non-steady state calculations arepreferably performed for each second after the start of the noble metalapplication process. The output of the simulation model may be storedand plotted, for example, for each five minute interval in a simulatedforty-eight hour application process period. A forty-eight hoursimulation may be based on a set of step-wise inputs, as mentionedabove. The user may select or change the time, Δt, between inputtingsample data in order to check convergence. With the present arrangement,the user is provided easy access to the kinetic parameters used tocalculate rate constants, equivalent conductance constants, and allother chemical parameters, so that they can be changed from a set ofdefault values. For example, individual default parameters may beselectively displayed prominently on the output display device so thatthe user can easily restore them to the default values. The input fileand simulation results (tables and charts) may also be copied, forexample, to a separate Excel™ workbook.

Standard statistical analysis charts may be input by the user, forexample, in an Excel™ workbook, along with the stored numeric results.Such standard charts may include information specifying, for example:

1. noble metal loading (1 five-curve chart for Pt and 1 for Rh versustime at two sample locations, bottom head, inner shroud, outer shroud).

2. Active noble metal concentrations (1 chart for Pt and Rh versus timeat two sample locations).

3. Inactive noble metal concentrations (1 chart for Pt and Rh versustime at two sample locations).

4. Concentrations of ions (two charts for all ion concentrations versustime, one per sample location).

5. Conductivity (1 chart of conductivity versus time at two samplelocations).

6. pH at 25 C. (1 chart of pH versus time at two sample locations).

7. Mass balance (2 charts for the sample locations, with curves of Rhloss, Pt loss, and %s unaccounted for based on other speciesconcentrations).

8. Ionic balance (1 chart for net charge versus time at the samplelocations)

The user may also make additional charts, for example, from thespreadsheets. A small window(s) in the computer display or printedoutput may be used to provide current values of critical results, e.g.,gmsPt/min, loading rates, % unaccounted for, conductivity, hrs tomaximum conductivity, hrs to loading targets (Pt and Rh), etc. Suchwindow contents may be defined as desired by the user. For the presentexample embodiment, the two sides of the reactor are assumed to beidentical and a new forty-eight hour run is computed and stored wheneverthe user changes the inputs.

The program code for the modeling/simulation routine of the presentinvention as illustrated in FIGS. 5A through 5E, may be written, forexample, in a Visual Basic module in an Excel workbook. Sample data maybe collected in the field and may be input to the modeling/simulationprogram from a spreadsheet. Such data may include measurements, forexample, from GFAA (soluble Pt and Rh), zinc, IC ions, conductivity, pH,temperature, etc. The spreadsheet may be formatted so that its contentscan easily be added to selected graphs generated as output by themodeling/simulation program.

The following list provides a non-comprehensive listing of exampleregions and sub-regions of a reactor that may be modeled using thepresent invention:

Region Sub-region Fuel Fuel channel Region H fuel channel Core bypassCore bypass, g Region H bypass Outer bypass Outer bypass Region H outerbypass Upper plenum Upper plenum Steam separator Steam separator region1 Steam separator region 2 Steam separator region 3 Steam separatorregion 4 Steam separator region 5 Steam separator region 6 Mixing plenumMixing plenum, above feedwater mix Mixing plenum, below feedwater mixDowncomer Downcomer, s1 start Downcomer, s1 carry under Downcomer, s2 +s31 Downcomer, s32 + s4 + s5 Recirculation Recirculation suction pipeRecirculation discharge pipe Recirculation header ring Recirculationriser pipe Recirculation jet pump internal riser Recirc jet pump nozzle(rams head) Jet pump Jet pump, throat Jet pump, diffuser Jet pump,tailpiece Lower plenum Lower plenum, down-flow Lower plenum, up-flowbelow core plate Lower plenum, up-flow above core plate Sample line ASample line, 1st section Sample line, 2nd section Sample line, 3rdsection Sample line B Sample line, 1st section Sample line, 2nd sectionSample line, 3rd section

The modeling program/routine of the present invention may also be usedto perform non-steady state evaluations of water chemistry transients inBWRs. For example, concentrations of water impurities in a BWR due toleaking fuel rods, corroding components or other intrusions can beeasily modeled by including “source” terms in the modeling routine torepresent an impurities at probable locations that might account fortheir appearance. Likewise, the disappearance of various impurities, forexample, due to incorporation into crud or radioactive decay, can beaccounted for by including representative “sink” terms in the modelingroutine. In this manner, the non-steady state concentration ofradioactive isotopes, corrosion products and water impurities could bedetermined for the entire water flow circuit(s) throughout the reactorand in the steam for performing, for example, analysis on fuel leaks andcorrosion.

The foregoing method and apparatus has been disclosed for the purpose ofillustration. As should be obvious to one of ordinary skill in the art,the noble metal application process modeling program routines of thepresent invention could be adapted, with only slight modifications, tomodel other non-steady state fluid systems having flow loops thatcontain multiple regions of disparate geometry and parallel flow paths.Variations and modifications of the disclosed invention will be readilyapparent to computer programming practitioners of ordinary skill orthose skilled in the arts of boiling-water nuclear reactor operationand/or other non-steady state physical chemistry systems.

While the invention has been described in connection with what ispresently considered to be the most practical and preferred embodiment,it is to be understood that the invention is not to be limited to thedisclosed embodiment, but on the contrary, is intended to cover variousmodifications and equivalent arrangements included within the spirit andscope of the appended claims.

What is claimed is:
 1. A method of modeling noble metal loadingreactions for a noble metal deposition process throughout a water flowcircuit of a nuclear reactor, comprising the steps of: dividing theprimary water circuit into a plurality of separate regions eachcomprising a plurality of cells of equal flow residence time; performinga mass balance evaluation for each individual cell; determining noblemetal concentrations and surface loadings in each cell using chemicalkinetic equations based on local reaction rate constants for each cell;sampling the reactor water at one or more selected locations throughoutthe water flow circuit to determine concentrations of noble metals ateach sample location; and updating one or more values used for localreaction rate constants based on sampled concentrations from saidselected locations.
 2. A method for modeling noble metal loadingoccurring within a water flow circuit for a nuclear reactor during anoble metal deposition process, comprising the steps performed by acomputer of: a) dividing the water flow circuit into a plurality ofseparate regions each comprising a plurality of cells of equal flowresidence time; b) determining noble metal concentrations and surfaceloadings in each cell using chemical kinetic equations based on localreaction rate constants for each cell; and c) updating one or morevalues used for local reaction rate constants based on sampled noblemetal concentrations obtained from said selected locations within thewater flow circuit.
 3. A method of maintaining proper noble metalloading within a primary water flow circuit for a nuclear reactor forperforming a noble metal deposition process, comprising the steps of: a)obtaining data representing the initial state of the reactor waterchemistry and initial operating conditions of the reactor; b) using acomputer to model noble metal loading throughout the primary water flowcircuit, wherein noble metal loading reactions are modeled by dividingthe primary water circuit into a plurality of separate regions eachcomprising a plurality of cells of equal flow residence time andperforming a mass balance evaluation for each individual cell; c)sampling the reactor water at one or more selected locations throughoutthe water flow circuit and measuring concentrations of noble metals foreach sample; d) comparing measured concentrations of noble metals fromeach sample with concentration values produced by the computer modelingin step (b); e) calibrating a computer model used in computing noblemetal reactions by altering values of reaction rate constants used bythe computer model until the model results agree with the samples; andf) altering the operating conditions of the reactor if subsequentloading rates determined by the computer model are inconsistent withpredetermined target goals.
 4. The method as defined in claim 3, whereinmodeling of noble metal loading is performed using a portable computer.5. The method as defined in claim 3, wherein a computer modeling of thenoble metal deposition also models reactor water chemistry, pH, andconductivity.
 6. A method for controlling the amount of noble metalatoms deposited over time into an oxide layer present on a metal surfaceof an object in contact with a high temperature fluid containing acompound having said metal atoms, which metal atoms increase thecorrosion resistance of said metal surface when present in the oxidefilm, said method comprising the steps of: a) using a computer to modelnoble metal loading in the fluid; b) sampling the fluid at one or moreselected times during deposition and measuring concentrations of noblemetals at each sample time; d) comparing measured concentrations ofnoble metals from at least one sample with concentration values computedby the computer model; e) calibrating the computer model by alteringvalues of reaction rate constants used by the computer model until themodel results agree with the sampled concentrations; and f) alteringtemperature conditions and/or noble metal concentrations in the fluid ifsubsequent loading rates determined by the computer model areinconsistent with predetermined deposition goals.